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Necessary and sufficient conditions for latent separability

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  • Ian Crawford

Abstract

This paper extends the nonparametric methods developed by Samuelson (1948), Houthakker (1950), Afriat (1973), Diewert (1973) and Varian (1982, 1983) to latently separable models. It presents necessary and sufficient empirical conditions under which data on the market behaviour of a price-taking consumer, and a hypothesised allocation across latent groups are nonparametrically consistentwith latent separability (Gorman (1968, 1978), Blundell and Robin (2000)). It considers homothetic latent separability and weak separability as special cases.

Suggested Citation

  • Ian Crawford, 2004. "Necessary and sufficient conditions for latent separability," CeMMAP working papers 02/04, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:02/04
    DOI: 10.1920/wp.cem.2004.0204
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    References listed on IDEAS

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    1. Richard Blundell & Jean-Marc Robin, 2000. "Latent Separability: Grouping Goods without Weak Separability," Econometrica, Econometric Society, vol. 68(1), pages 53-84, January.
    2. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    3. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 99-110.
    4. repec:hal:spmain:info:hdl:2441/f0uohitsgqh8dhk9820172631 is not listed on IDEAS
    5. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
    6. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 419-425.
    7. Afriat, S N, 1973. "On a System of Inequalities in Demand Analysis: An Extension of the Classical Method," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 460-472, June.
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    Cited by:

    1. Cherchye, L.J.H. & Crawford, I. & de Rock, B. & Vermeulen, F.M.P., 2011. "Aggregation without the Aggravation? Nonparametric Analysis of the Representative Consumer," Other publications TiSEM e6102eac-a248-49dc-ae8e-1, Tilburg University, School of Economics and Management.
    2. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    3. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Hjertstrand, Per, 2015. "Revealed preference tests for weak separability: An integer programming approach," Journal of Econometrics, Elsevier, vol. 186(1), pages 129-141.
    4. Laura Blow & Martin Browning & Ian Crawford, 2008. "Revealed Preference Analysis of Characteristics Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 371-389.
    5. Dieter Saelens, 2022. "Unitary or collective households? A nonparametric rationality and separability test using detailed data on consumption expenditures and time use," Empirical Economics, Springer, vol. 62(2), pages 637-677, February.

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